Thermochemistry

Thermochemistry studies the energy changes that accompany chemical reactions. Key concepts:

• The system is the part of the universe being studied (usually the reactants and products). Everything else is the surroundings.
• The first law of thermodynamics (conservation of energy) states that energy cannot be created or destroyed, only transferred or converted: ΔU = q + w, where q is heat and w is work.
• Heat (q) flows from hot to cold. When q is negative, heat flows out of the system (exothermic); when positive, heat flows in (endothermic).

Enthalpy (H) is a state function defined as H = U + PV. For reactions at constant pressure, the enthalpy change ΔH equals the heat exchanged: ΔH = q_p. Exothermic reactions have ΔH < 0; endothermic reactions have ΔH > 0.

The relationship between heat transferred and temperature change is governed by specific heat capacity (c) — the amount of heat needed to raise 1 gram of a substance by 1 °C.

The equation: q = mcΔT

• q = heat transferred (J)
• m = mass (g)
• c = specific heat (J/g·°C). Water’s specific heat is 4.184 J/g·°C.
• ΔT = T_final − T_initial (°C)

If q is positive, the substance absorbed heat (temperature rose). If q is negative, the substance released heat (temperature dropped).

Heat capacity (C) is the heat needed to raise the temperature of an entire object by 1 °C: q = CΔT. Specific heat is heat capacity per gram.

Calorimetry measures heat changes by using an insulated container (calorimeter). The principle: heat lost by one substance equals heat gained by another (conservation of energy).

In a coffee-cup calorimeter (constant pressure): a reaction occurs in solution, and the temperature change of the solution is measured. Then q_rxn = −q_solution = −mcΔT. Dividing by moles gives ΔH per mole.

In a bomb calorimeter (constant volume): a substance is burned in a sealed steel container surrounded by water. The heat released raises the water temperature: q_rxn = −C_cal × ΔT, where C_cal is the calorimeter’s heat capacity.

Example: If 50.0 g of water rises 6.0 °C during a reaction, q_water = (50.0)(4.184)(6.0) = 1255 J, so q_rxn = −1255 J.

An energy diagram (enthalpy diagram) plots the energy of reactants and products on a vertical axis:

• Exothermic reactions: products are lower in energy than reactants. The arrow points downward, and ΔH is negative. Energy is released to the surroundings.
• Endothermic reactions: products are higher in energy than reactants. The arrow points upward, and ΔH is positive. Energy is absorbed from the surroundings.

The activation energy (E_a) is the energy barrier between reactants and the transition state — the minimum energy needed for the reaction to proceed. Even exothermic reactions require some activation energy to get started.

Hess’s law states that the enthalpy change for an overall reaction is the sum of the enthalpy changes for the individual steps, regardless of the pathway taken. This is because enthalpy is a state function — it depends only on the initial and final states.

To use Hess’s law: (1) Arrange given equations so that when added, reactants and products match the target equation. (2) If an equation is reversed, change the sign of ΔH. (3) If an equation is multiplied by a factor, multiply ΔH by that factor. (4) Add all ΔH values.

This method lets us calculate ΔH for reactions that are difficult to measure directly by combining reactions that are easy to measure.

The standard enthalpy of formation (ΔH°_f) is the enthalpy change when exactly 1 mole of a compound is formed from its elements in their standard states (pure form at 25 °C and 1 atm). For example, the standard state of oxygen is O₂(g), carbon is C(s, graphite), and iron is Fe(s). By convention, ΔH°_f for any element already in its standard state is exactly zero.

This convention makes formation values powerful: the enthalpy of any reaction can be calculated from a table of ΔH°_f values using:

ΔH°_rxn = ∑ n·ΔH°_f(products) − ∑ n·ΔH°_f(reactants)

where n is the stoichiometric coefficient of each species in the balanced equation. This relationship follows directly from Hess’s law — every reaction can be imagined as decomposing reactants into elements, then recombining those elements into products.

Example: For CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(l), ΔH° = [ΔH°_f(CO₂) + 2·ΔH°_f(H₂O)] − [ΔH°_f(CH₄) + 2·ΔH°_f(O₂)]. Because ΔH°_f(O₂) = 0, only three table values are needed.

Bond energy is the energy required to break one mole of a particular bond in the gas phase. It can be used to estimate ΔH for gas-phase reactions:

ΔH ≈ ∑(bonds broken) − ∑(bonds formed)

Breaking bonds requires energy (positive), forming bonds releases energy (negative). If more energy is released in forming new bonds than consumed in breaking old ones, the reaction is exothermic.

Stoichiometric enthalpy calculations use ΔH as a conversion factor, just like mole ratios. If ΔH = −890 kJ for the combustion of 1 mol CH₄, then burning 2.5 mol produces q = 2.5 × (−890) = −2225 kJ. You can also convert between grams, moles, and energy.

Choose the right approach by identifying what information is given:

1. Temperature change measured? Use q = mcΔT (calorimetry).
2. Standard enthalpies of formation available? Use ΔH°_rxn = ΣΔH°_f(products) − ΣΔH°_f(reactants).
3. Need to combine reactions? Use Hess’s law: reverse, multiply, and add reactions until the target equation is obtained.
4. Bond energies given? Use ΔH ≈ Σ(bonds broken) − Σ(bonds formed). This is approximate and applies to gas-phase reactions.
5. Stoichiometric conversion? ΔH applies to the equation as written. Scale it with the mole ratio.

Common mistakes: confusing the sign of ΔH (negative = exothermic, positive = endothermic), forgetting that ΔH°_f for elements in their standard state is zero, using bond energies for condensed-phase reactions where they don’t apply well, reversing a reaction without changing the sign of ΔH, and using mass of solution instead of mass of solute (or vice versa) in calorimetry.